A035601 Number of points of L1 norm 7 in cubic lattice Z^n.

0, 2, 28, 198, 952, 3530, 10836, 28814, 68464, 148626, 299660, 568150, 1022760, 1761370, 2919620, 4680990, 7288544, 11058466, 16395516, 23810534, 33940120, 47568618, 65652532, 89347502, 120037968, 159369650, 209284972

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - N. J. A. Sloane, Feb 13 2013

M. Janjic, B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5.

Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = (8*n^6 + 4*5*7*n^4 + 8*7*7*n^2 + 2*5*9)*n/(5*7*9). - Frank Ellermann, Mar 16 2002

G.f.: 2*x*(1+x)^6/(1-x)^8. - Colin Barker, Apr 15 2012

a(n) = 2*A099193(n). - R. J. Mathar, Dec 10 2013

Maple

f := proc(d, m) local i; sum( 2^i*binomial(d, i)*binomial(m-1, i-1), i=1..min(d, m)); end; # n=dimension, m=norm

Mathematica

CoefficientList[Series[2*x*(1+x)^6/(1-x)^8, {x, 0, 30}], x] (* Vincenzo Librandi, Apr 23 2012 *)

Prog

(PARI) (8*n^7+140*n^5+392*n^3+90*n)/315 \\ Charles R Greathouse IV, Dec 07 2011
(Magma) [( 8*n^6 +4*5*7*n^4 +8*7*7*n^2 +2*5*9 )*n/(5*7*9): n in [0..30]]; // Vincenzo Librandi, Apr 23 2012

Crossrefs

Cf. A035596-A035607.

Sequence in context: A065340 A001798 A123787 * A281124 A244721 A001759

Adjacent sequences: A035598 A035599 A035600 * A035602 A035603 A035604

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved